JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry QA part 11/ JEE Question on distance of a point from a plane measured parallel to a given line solved with the related concepts

1. Physics Helpline
L K Satapathy
3D Geometry QA 11

2. Physics Helpline
L K Satapathy
3 D Geometry QA 11
Question: The distance of the point (1 , – 5 , 9) from the plane x – y + z = 5
measured parallel to the line x = y = z is
10 20( ) 3 10 ( ) 10 3 ( ) ( )
33
a b c d
Answer :
The given point P = (1 , – 5 , 9)
Equation of the given line is
00 0 . . . (1)
1 1 1
yx z   
Equation of the line passing through P and parallel to line (1) is
51 9 . . . (2)
1 1 1
yx z 
   
 Coordinates of any point on line (2) ( 1, 5 , 9)     
x y z  (1, 5,9)P 
Q
x y z 

3. Physics Helpline
L K Satapathy
3 D Geometry QA 11
Correct option = (b)
If this point lies on the plane x – y + z = 5 , then
( 1) ( 5) ( 9) 5       
Let Q be the point of intersection of line (2) and the plane
Then the coordinates of Q ( 1, 5 , 9) ( 9, 15, 1)         
 Distance between P (1 , – 5 , 9) and Q ( – 9 , – 15 , – 1 )
2 2 2
(1 9) ( 5 15) (9 1)      
15 5 10      
300 10 3 

4. Physics Helpline
L K Satapathy
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